Lecture 04_Chapter5_Elasticity & Its Application

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Elasticity and its

Application

E

conomics

P R I N C I P L E S O FP R I N C I P L E S O F

N. Gregory Mankiw

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by Ron Cronovich

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In this chapter,

look for the answers to these

questions:



_{What is elasticity? What kinds of issues can}

elasticity help us understand?



What is the price elasticity of demand? How is it related to the demand curve?

How is it related to revenue & expenditure?



What is the price elasticity of supply? How is it related to the supply curve?

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You design websites for local businesses.

You charge $200 per website,

and currently sell 12 websites per month.

Your costs are rising

(including the opportunity cost of your time),

so you consider raising the price to $250.

The law of demand says that you won’t sell as

many websites if you raise your price.

How many fewer websites? How much will your

revenue fall, or might it increase?

You design websites for local businesses.

You charge $200 per website,

and currently sell 12 websites per month.

Your costs are rising

(including the opportunity cost of your time),

so you consider raising the price to $250.

The law of demand says that you won’t sell as

many websites if you raise your price.

How many fewer websites? How much will your

revenue fall, or might it increase?

A scenario…

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Elasticity



Basic idea:

Elasticity measures how much one variable

responds to changes in another variable.



One type of elasticity measures how much demand for your websites will fall if you raise your price.



Definition:

Elasticity

is a numerical measure of the

responsiveness of

Q

d

or

Q

s

to one of its

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ELASTICITY AND ITS APPLICATION 5

Price Elasticity of Demand



Price elasticity of demand

measures how

much

Q

d

responds to a change in

P

.

Price elasticity

of demand =

Percentage change in Qd

Percentage change in P

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Price Elasticity of Demand

equals

P

Q D

Q₂ P₂

P₁

Q₁ P rises

by 10%

Q falls by 15%

15%

10% = 1.5

Price elasticity

of demand =

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ELASTICITY AND ITS APPLICATION 7

Price Elasticity of Demand

Along a D curve, P and Q

move in opposite directions, which would make price

elasticity negative.

We will drop the minus sign and report all price

elasticities as

positive numbers.

Along a D curve, P and Q

move in opposite directions, which would make price

elasticity negative.

We will drop the minus sign and report all price

elasticities as positive numbers. P Q D Q₂ P₂ P₁ Q₁ Price elasticity

of demand =

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Calculating Percentage

Changes

P

Q D

$250

8 B

$200

12 A

Demand for your websites

Standard method of computing the

percentage (%) change:

end value – start value

start value x 100%

Going from A to B,

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ELASTICITY AND ITS APPLICATION 9

Calculating Percentage

Changes

P

Q D

$250

8 B

$200

12 A

Demand for your websites

Problem:

The standard method gives different answers depending on where you start.

From A to B,

P rises 25%, Q falls 33%, elasticity = 33/25 = 1.33

From B to A,

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Calculating Percentage

Changes



So, we instead use the midpoint method:

end value – start value

midpoint

x 100%



The midpoint is the number halfway between the start & end values, the average of those values.

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ELASTICITY AND ITS APPLICATION 11

Calculating Percentage

Changes



Using the midpoint method, the % change in P equals

$250 – $200

$225

x 100% = 22.2%



The % change in Q equals

12 – 8

10

x 100% = 40.0%



The price elasticity of demand equals

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A C T I V E L E A R N I N G

1

Calculate an elasticity

Use the following information to

calculate the price elasticity of demand

for hotel rooms:

if P = $70, Qd = 5000

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1

Answers

13

Use midpoint method to calculate

% change in

Q

d

(5000 – 3000)/4000 =

50%

% change in

P

($90 – $70)/$80 =

25%

The price elasticity of demand equals

50%

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What determines price

elasticity?

To learn the determinants of price elasticity,

we look at a series of examples.

Each compares two common goods.

In each example:



Suppose the prices of both goods rise by 20%.



The good for which Qd falls the most (in percent)

has the highest price elasticity of demand. Which good is it? Why?

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ELASTICITY AND ITS APPLICATION 15

EXAMPLE 1:

Breakfast cereal vs. Sunscreen



The prices of both of these goods rise by 20%. For which good does

Q

d_{drop the most? Why?}



Breakfast cereal has close substitutes

(e.g., pancakes, Eggo waffles, leftover pizza), so buyers can easily switch if the price rises.



Sunscreen has no close substitutes, so consumers would probably not buy much less if its price rises.

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EXAMPLE 2:

“Blue Jeans” vs. “Clothing”



The prices of both goods rise by 20%.

For which good does

Q



For a narrowly defined good such as blue jeans, there are many substitutes (khakis, shorts, Speedos).



There are fewer substitutes available for broadly defined goods.

(There aren’t too many substitutes for clothing, other than living in a nudist colony.)

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ELASTICITY AND ITS APPLICATION 17

EXAMPLE 3:

Insulin vs. Caribbean Cruises



The prices of both of these goods rise by 20%. For which good does

Q



To millions of diabetics, insulin is a necessity. A rise in its price would cause little or no

decrease in demand.



A cruise is a luxury. If the price rises, some people will forego it.

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EXAMPLE 4:

Gasoline in the Short Run vs.

Gasoline in the Long Run



The price of gasoline rises 20%. Does Qd drop

more in the short run or the long run? Why?



There’s not much people can do in the

short run, other than ride the bus or carpool.



In the long run, people can buy smaller cars or live closer to where they work.

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ELASTICITY AND ITS APPLICATION 19

The Determinants of Price

Elasticity:

A Summary

The price elasticity of demand depends on:



the extent to which close substitutes are

available



whether the good is a necessity or a luxury



how broadly or narrowly the good is defined



the time horizon – elasticity is higher in the

long run than the short run

The price elasticity of demand depends on:



the extent to which close substitutes are

available



whether the good is a necessity or a luxury



how broadly or narrowly the good is defined

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The Variety of Demand

Curves



The price elasticity of demand is closely related

to the slope of the demand curve.



Rule of thumb:

The flatter the curve, the bigger the elasticity.

The steeper the curve, the smaller the elasticity.

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ELASTICITY AND ITS APPLICATION 21

Q₁ P₁

D

“Perfectly inelastic demand”

(one

extreme case)

P

Q P₂

P falls by 10%

Q changes by 0% 0%

10% = 0

= % change in Q

% change in P =

Consumers’

price sensitivity:

D curve:

Elasticity:

vertical

none

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D

“Inelastic demand”

P

Q Q₁

P₁

Q₂ P₂

Q rises less < 10%

10% < 1

= % change in Q

% change in P =

P falls by 10%

Consumers’

price sensitivity:

D curve:

Elasticity:

relatively steep

relatively low

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ELASTICITY AND ITS APPLICATION 23

D

“Unit elastic

demand”

P

Q Q₁

P₁

Q₂ P₂

Q rises by 10% 10%

10% = 1

= % change in Q

% change in P =

P falls by 10%

Consumers’

price sensitivity:

Elasticity:

intermediate

1

D curve:

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D

“Elastic demand”

P

Q Q₁

P₁

Q₂ P₂

Q rises more > 10%

10% > 1

= % change in Q

% change in P =

P falls by 10%

Consumers’

price sensitivity:

D curve:

Elasticity:

relatively flat

relatively high

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ELASTICITY AND ITS APPLICATION 25

D

“Perfectly elastic demand”

(the other

extreme)

P

Q P₁

Q₁ P changes

by 0%

Q changes by any % any %

0% = infinity

Q₂ P₂ =

Consumers’

price sensitivity:

D curve:

Elasticity: infinity horizontal extreme Price elasticity of demand

= % change in Q

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Elasticity of a Linear Demand

Curve

The slope of a linear demand curve is constant, but its

elasticity is not.

P

Q

$30

20

10

$0

0 20 40 60

200%

40% = 5.0

E =

67%

67% = 1.0

E =

40%

200% = 0.2

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ELASTICITY AND ITS APPLICATION 27

Price Elasticity and Total

Revenue



Continuing our scenario, if you raise your price

from $200 to $250, would your revenue rise or fall?

Revenue = P x Q



A price increase has two effects on revenue:



Higher P means more revenue on each unit you sell.



But you sell fewer units (lower Q), due to Law of Demand.



Which of these two effects is bigger?

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Price Elasticity and Total

Revenue



If demand is elastic, then

price elast. of demand > 1

% change in

Q

> % change in

P



The fall in revenue from lower

Q

is greater

than the increase in revenue from higher

P

,

so revenue falls.

Revenue = P x Q

Price elasticity of demand =

Percentage change in Q

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ELASTICITY AND ITS APPLICATION 29

Price Elasticity and Total

Revenue

Elastic demand

(elasticity = 1.8) _P

Q D

$200

12

If P = $200,

Q = 12 and

revenue = $2400.

When D is elastic, a price increase

causes revenue to fall.

$250

8

If P = $250,

Q = 8 and

revenue = $2000.

lost

revenue due to lower Q

increased revenue due to higher P

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Price Elasticity and Total

Revenue



If demand is inelastic, then price elast. of demand < 1

% change in Q < % change in P



The fall in revenue from lower Q is smaller than the increase in revenue from higher P, so revenue rises.



In our example, suppose that Q only falls to 10 Revenue = P x Q

Price elasticity of demand =

Percentage change in Q

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ELASTICITY AND ITS APPLICATION 31

Price Elasticity and Total

Revenue

Now, demand is inelastic:

elasticity = 0.82 _P

Q D

$200

12

If P = $200,

Q = 12 and

revenue = $2400. $250

10

If P = $250,

Q = 10 and

revenue = $2500. When D is inelastic, a price increase

causes revenue to rise.

lost

revenue due to lower Q

increased revenue due to higher P

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A.

Pharmacies raise the price of insulin by 10%.

Does total expenditure on insulin rise or fall?

B.

As a result of a fare war, the price of a luxury

cruise falls 20%.

Does luxury cruise companies’ total revenue

rise or fall?

2

Elasticity and

expenditure/revenue

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2

Answers

33

A.

Pharmacies raise the price of insulin by 10%.

Does total expenditure on insulin rise or fall?

Expenditure =

P

x

Q

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2

Answers

B.

As a result of a fare war, the price of a luxury

cruise falls 20%.

Does luxury cruise companies’ total revenue

rise or fall?

Revenue =

P

x

Q

The fall in

P

reduces revenue,

but

Q

increases, which increases revenue.

Which effect is bigger?

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ELASTICITY AND ITS APPLICATION 35

APPLICATION:

Does Drug Interdiction

Increase or Decrease Drug-Related

Crime?



One side effect of illegal drug use is crime:

Users often turn to crime to finance their habit.



We examine two policies designed to reduce

illegal drug use and see what effects they have

on drug-related crime.



For simplicity, we assume the total dollar value

of drug-related crime equals total expenditure

on drugs.

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D₁

Policy 1: Interdiction

Price of Drugs Quantity of Drugs S₁ S₂ P₁ Q₁ P₂ Q₂ Interdiction reduces the supply of drugs. Since demand for drugs is

inelastic,

P rises propor-tionally more than Q falls.

Result: an increase in total spending on drugs, and in drug-related crime

new value of drug-related crime

initial value of

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ELASTICITY AND ITS APPLICATION 37

Policy 2: Education

Price of Drugs Quantity of Drugs D₁ S P₁ Q₁ D₂ P₂ Q₂ Education reduces the demand for drugs.

P and Q fall.

Result:

A decrease in total spending on drugs, and in drug-related crime. initial value of drug-related crime new value of

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Price Elasticity of Supply



Price elasticity of supply

measures how much

Q

s

responds to a change in

P

.

Price elasticity

of supply =

Percentage change in Qs



Loosely speaking, it measures sellers’

price-sensitivity.

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ELASTICITY AND ITS APPLICATION 39

Q₂

Price Elasticity of Supply

Price

elasticity of supply equals

P

Q S

P₂

Q₁ P₁

P rises by 8%

Q rises by 16%

16%

8% = 2.0

Price elasticity

of supply =

Percentage change in Qs

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The Variety of Supply Curves



The slope of the supply curve is closely related to

price elasticity of supply.



Rule of thumb:

The flatter the curve, the bigger the elasticity.

The steeper the curve, the smaller the elasticity.

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ELASTICITY AND ITS APPLICATION 41

S

“Perfectly inelastic”

(one extreme)

P

Q Q₁

P₁ P₂

Q changes by 0%

0%

10% = 0

= % change in Q

% change in P =

P rises by 10%

Sellers’

price sensitivity:

S curve:

Elasticity:

vertical

none

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S

“Inelastic”

P

Q Q₁

P₁

Q₂ P₂

Q rises less < 10%

10% < 1

= % change in Q

% change in P =

P rises by 10%

Sellers’

price sensitivity:

S curve:

Elasticity:

relatively steep

relatively low

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ELASTICITY AND ITS APPLICATION 43

S

“Unit elastic”

P

Q Q₁

P₁

Q₂ P₂

Q rises by 10%

10%

10% = 1

= % change in Q

% change in P =

P rises by 10%

Sellers’

price sensitivity:

S curve:

Elasticity:

intermediate slope

intermediate

(44)

S

“Elastic”

P

Q Q₁

P₁

Q₂ P₂

Q rises more > 10%

10% > 1

= % change in Q

% change in P =

P rises by 10%

Sellers’

price sensitivity:

S curve:

Elasticity:

relatively flat

relatively high

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ELASTICITY AND ITS APPLICATION 45

S

“Perfectly elastic”

(the other

extreme)

P

Q P₁

Q₁ P changes

by 0%

Q changes by any % any %

0% = infinity

= % change in Q

% change in P =

Q₂ P₂ =

Sellers’

price sensitivity:

S curve:

Elasticity:

horizontal

extreme

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The Determinants of Supply

Elasticity



The more easily sellers can change the quantity

they produce, the greater the price elasticity of

supply.



Example: Supply of beachfront property is harder to vary and thus less elastic than supply of new cars.



For many goods, price elasticity of supply

is greater in the long run than in the short run,

because firms can build new factories,

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3

Elasticity and changes in

equilibrium

47



The supply of beachfront property is inelastic.

The supply of new cars is elastic.



Suppose population growth causes

demand for both goods to double

(at each price,

Q

d

doubles).



For which product will

P

change the most?

(48)

3

Answers

Beachfront property

(inelastic supply):

P

Q

D₁ S

P₁ A

When supply is inelastic,

an increase in demand has a bigger impact on price than on quantity.

D₂

B

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3

Answers

49

New cars

(elastic supply):

P

Q

D₁

S

Q₁

P₁ A

When supply is elastic,

an increase in demand has a bigger impact on quantity than on price.

D₂

Q₂

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S

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ELASTICITY AND ITS APPLICATION 51

Other Elasticities



Income elasticity of demand: measures the response of Qd to a change in consumer income

Income elasticity of demand =

Percent change in Qd

Percent change in income



Recall from Chapter 4: An increase in income

causes an increase in demand for a normal good.



Hence, for normal goods, income elasticity > 0.

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Other Elasticities



Cross-price elasticity of demand:

measures the response of demand for one good to changes in the price of another good

Cross-price elast. of demand =

% change in Qd for good 1

% change in price of good 2



For substitutes, cross-price elasticity > 0

(e.g., an increase in price of beef causes an increase in demand for chicken)



For complements, cross-price elasticity < 0

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CHAPTER SUMMARY



Elasticity measures the responsiveness of

Qd or Qs to one of its determinants.



Price elasticity of demand equals percentage

change in Qd divided by percentage change in P.

When it’s less than one, demand is “inelastic.” When greater than one, demand is “elastic.”



When demand is inelastic, total revenue rises when price rises. When demand is elastic, total revenue falls when price rises.

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CHAPTER SUMMARY



Demand is less elastic in the short run,

for necessities, for broadly defined goods, or for goods with few close substitutes.



Price elasticity of supply equals percentage

change in Qs divided by percentage change in P.

When it’s less than one, supply is “inelastic.” When greater than one, supply is “elastic.”

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CHAPTER SUMMARY



The income elasticity of demand measures how

much quantity demanded responds to changes in

buyers’ incomes.



The cross-price elasticity of demand measures

how much demand for one good responds to

changes in the price of another good.